A win-win supply chain solution using project contracts with bargaining games

For product supply chains, contractual relationships that provide win-win outcomes between the supply chain members, have been found to offer optimum results. However, for bargaining situations where time/cost is the source of the uncertainty, i.e. projects, there is limited knowledge available on how contracts can be used to establish win-win relations. This paper investigates whether cost-sharing project contracts can establish a win-win solution in project supply chains where the project manager is risk-neutral and the contractor is risk-averse. The paper examines how the theory can be extended beyond the symmetrical normal distributions to asymmetrical beta and gamma distributions that are more appropriate, and so more often used, for project completion times. Besides using the Nash bargaining approach for analyzing the bargaining process, the paper also analyzes the bargaining problems using the Kalai-Smorodinsky and Utilitarian approaches to bargaining. It was found that the solutions from cost-plus contracts dominate any other form of cost-sharing contract, and so they provide a win-win solution for both members of the supply chain for the cases of Nash and Kalai-Smorodinsky bargaining. However, this is not the case for Utilitarian bargaining. A numerical exercise was conducted to investigate the results and implications of how the models would work in practice. The research shows that from a theoretical perspective, cost-plus contracts are the optimal bargaining solution not only when using a normal distribution, but also when using more appropriate asymmetrical distributions. This optimality is robust for the Nash and Kalai-Smorodinsky bargaining approaches, but not for the Utilitarian approach whose sensitivity to noise makes it an inappropriate choice here.